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Practical Witness-Key-Agreement for Blockchain-Based Dark Pools Financial Trading

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Financial Cryptography and Data Security (FC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12675))

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Abstract

We introduce a new cryptographic scheme, Witness Key Agreement (WKA), that allows a party to securely agree on a secret key with a counter party holding publicly committed information only if the counter party also owns a secret witness in a desired (arithmetic) relation with the committed information.

Our motivating applications are over-the-counter (OTC) markets and dark pools, popular trading mechanisms. In such pools investors wish to communicate only to trading partners whose transaction conditions and asset holdings satisfy some constraints. The investor must establish a secure, authenticated channel with eligible traders where the latter committed information matches a desired relation. At the same time traders should be able to show eligibility while keeping their financial information secret.

We construct a WKA scheme for languages of statements proven in the designated-verifier Succinct Zero-Knowledge Non-Interactive Argument of Knowledge Proof System (zk-SNARK). We illustrate the practical feasibility of our construction with some arithmetic circuits of practical interest by using data from US$ denominated corporate securities traded on Bloomberg Tradebook.

This research was conducted during the author’s visit to the University of Waterloo.

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Notes

  1. 1.

    WKA does not intend to hide whether the Prover/Verifier established communication as they are completely anonymous.

  2. 2.

    One can argue that there could be DDOS attacks where an attacker can post either malformed offers, or correctly formed ones but they have no intention of filling, to the blockchain. In the first case, as the Verifier only needs to forge the last proof element F (1) while the Prover has to compute the full proof (4(m − l + 3n)) as shown in Table 3, such an attack will require tremendous effort from the Prover but not so much from the Verifier. In the second case, unfortunately we cannot solve this as it exists even in the centralized system. A trader/investor can post an offer, and cancel it before it is filled or immediately in the next round. However, at the point the offer was posted, the exchange cannot know whether the offer will be canceled or not.

  3. 3.

    In the concrete construction by Groth [24] (see also Fig. 3), \(k = 3\) and the proof matrix \(\boldsymbol{\varPi }\) is represented as the coefficients of the linear functions.

  4. 4.

    The concrete example of this observation can be seen in Fig. 3 in Sect. 6. The first two elements A and B (Eq. (7) and (8)) uniquely define C (Eq. (9)) and they can be fed into the proof forging formula (Eq. (11)) to get the 3rd element C which should be the same for either party.

  5. 5.

    This property formally guarantees that given a valid ciphertext \(\boldsymbol{\pi }\) by an adversary, it is possible to efficiently extract the corresponding affine function \((\boldsymbol{\varPi },\boldsymbol{\pi }_0)\) that explains \(\boldsymbol{\pi }\). Such property is important for Knowledge Soundness of WKA.

  6. 6.

    Users are advised to run the shared secret through a hash function modelled as a random oracle before using it as a key for any other cryptosystem.

  7. 7.

    Such an assumption can be relaxed by asking a TTP to generate the CRS (such as Bloomberg itself). Using a TTP for bootstrapping security protocols have been considered in literature, see for example HAWK [29]. This is a much weaker trust assumption than managing orders themselves because the generation of the CRS requires only the relation R and the public key for the encryption. Therefore such a TTP is only trusted to do the computation correctly. Without the private key, the TTP cannot learn additional information.

  8. 8.

    Benchmarked in 2015. As such, it provides a lower bound to our WKA performance.

  9. 9.

    https://ethstats.net/.

  10. 10.

    In our protocol, the blockchain is the actual bottleneck. Looking at Table 4, the runtime of each step (including setups) is less than the block time of the fastest permissionless blockchain (Ethereum roughly generates a block every 15 s). Hence evaluating the interfaces of our scheme with the blockchain is equivalent to evaluating the blockchain itself. We should add that the current blockchain technologies is not adequate yet for high speed dark pools. Our major concern and main evaluation focus therefore is our scheme’s crypto overhead.

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Acknowledgements

We thank Ian Goldberg, Ivan Visconti, and the anonymous reviewers for their many insightful comments and suggestions. Chan Nam Ngo and Fabio Massacci were partly supported by the European Commission under the H2020 Programme Grant Agreement No. 830929 (CyberSec4Europe). Florian Kerschbaum was supported by NSERC grants RGPIN-05849, CRDPJ-531191, IRC537591, and the Royal Bank of Canada.

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Authors and Affiliations

  1. University of Trento, Trento, Italy

    Chan Nam Ngo & Fabio Massacci

  2. Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Fabio Massacci

  3. University of Waterloo, Waterloo, Canada

    Florian Kerschbaum

  4. Durham Business School, Durham, UK

    Julian Williams

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  1. Chan Nam Ngo
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Correspondence to Chan Nam Ngo .

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Editors and Affiliations

  1. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Nikita Borisov

  2. KU Leuven, Leuven, Belgium

    Claudia Diaz

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Ngo, C.N., Massacci, F., Kerschbaum, F., Williams, J. (2021). Practical Witness-Key-Agreement for Blockchain-Based Dark Pools Financial Trading. In: Borisov, N., Diaz, C. (eds) Financial Cryptography and Data Security. FC 2021. Lecture Notes in Computer Science(), vol 12675. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64331-0_30

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